Other Situations Involving Group Matrices

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This chapter sketches various situations in which the tools described in this book have appeared. They are: 1.The characterization of those class functions on a group which are group characters.2.The use of group matrices in the theory of group rings.3.The application of group matrices to the theory of cogrowth of groups.4.Work of Poincaré on differential equations.5.The connection between factors of the group determinant and Chern classes.6.The appearance of the group matrix as a Gram matrix for tight frames with a symmetry group, which have appeared in the theory of wavelets.7.The theory of 3-manifolds.8.Control theory and electrical engineering.9.The algebra defined by considering the k-classes under multiplication.

Original languageEnglish (US)
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Pages313-340
Number of pages28
DOIs
StatePublished - Jan 1 2019

Publication series

NameLecture Notes in Mathematics
Volume2233
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692

Fingerprint

Matrix Groups
Gram Matrix
Tight Frame
Symmetry Group
Control Theory
Determinant
Multiplication
Algebra
Class

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Johnson, K. W. (2019). Other Situations Involving Group Matrices. In Lecture Notes in Mathematics (pp. 313-340). (Lecture Notes in Mathematics; Vol. 2233). Springer Verlag. https://doi.org/10.1007/978-3-030-28300-1_10
Johnson, Kenneth W. / Other Situations Involving Group Matrices. Lecture Notes in Mathematics. Springer Verlag, 2019. pp. 313-340 (Lecture Notes in Mathematics).
@inbook{ab8c67378f6e4200a6a03a594907810d,
title = "Other Situations Involving Group Matrices",
abstract = "This chapter sketches various situations in which the tools described in this book have appeared. They are: 1.The characterization of those class functions on a group which are group characters.2.The use of group matrices in the theory of group rings.3.The application of group matrices to the theory of cogrowth of groups.4.Work of Poincar{\'e} on differential equations.5.The connection between factors of the group determinant and Chern classes.6.The appearance of the group matrix as a Gram matrix for tight frames with a symmetry group, which have appeared in the theory of wavelets.7.The theory of 3-manifolds.8.Control theory and electrical engineering.9.The algebra defined by considering the k-classes under multiplication.",
author = "Johnson, {Kenneth W.}",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/978-3-030-28300-1_10",
language = "English (US)",
series = "Lecture Notes in Mathematics",
publisher = "Springer Verlag",
pages = "313--340",
booktitle = "Lecture Notes in Mathematics",
address = "Germany",

}

Johnson, KW 2019, Other Situations Involving Group Matrices. in Lecture Notes in Mathematics. Lecture Notes in Mathematics, vol. 2233, Springer Verlag, pp. 313-340. https://doi.org/10.1007/978-3-030-28300-1_10

Other Situations Involving Group Matrices. / Johnson, Kenneth W.

Lecture Notes in Mathematics. Springer Verlag, 2019. p. 313-340 (Lecture Notes in Mathematics; Vol. 2233).

Research output: Chapter in Book/Report/Conference proceedingChapter

TY - CHAP

T1 - Other Situations Involving Group Matrices

AU - Johnson, Kenneth W.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - This chapter sketches various situations in which the tools described in this book have appeared. They are: 1.The characterization of those class functions on a group which are group characters.2.The use of group matrices in the theory of group rings.3.The application of group matrices to the theory of cogrowth of groups.4.Work of Poincaré on differential equations.5.The connection between factors of the group determinant and Chern classes.6.The appearance of the group matrix as a Gram matrix for tight frames with a symmetry group, which have appeared in the theory of wavelets.7.The theory of 3-manifolds.8.Control theory and electrical engineering.9.The algebra defined by considering the k-classes under multiplication.

AB - This chapter sketches various situations in which the tools described in this book have appeared. They are: 1.The characterization of those class functions on a group which are group characters.2.The use of group matrices in the theory of group rings.3.The application of group matrices to the theory of cogrowth of groups.4.Work of Poincaré on differential equations.5.The connection between factors of the group determinant and Chern classes.6.The appearance of the group matrix as a Gram matrix for tight frames with a symmetry group, which have appeared in the theory of wavelets.7.The theory of 3-manifolds.8.Control theory and electrical engineering.9.The algebra defined by considering the k-classes under multiplication.

UR - http://www.scopus.com/inward/record.url?scp=85075130672&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85075130672&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-28300-1_10

DO - 10.1007/978-3-030-28300-1_10

M3 - Chapter

AN - SCOPUS:85075130672

T3 - Lecture Notes in Mathematics

SP - 313

EP - 340

BT - Lecture Notes in Mathematics

PB - Springer Verlag

ER -

Johnson KW. Other Situations Involving Group Matrices. In Lecture Notes in Mathematics. Springer Verlag. 2019. p. 313-340. (Lecture Notes in Mathematics). https://doi.org/10.1007/978-3-030-28300-1_10